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FIRST-PRINCIPLES STUDY OF ELECTRONIC AND VIBRATIONAL PROPERTIES OF BULK AND MONOLAYER V2O5

BHANDARI, CHURNA B
http://rave.ohiolink.edu/etdc/view?acc_num=case1459296089

Abstract Details

2016, Doctor of Philosophy, Case Western Reserve University, Physics.
Our main motivation for studying V$_2$O$_5$ is that it is a layered material and therefore potentially could have interesting different properties when made in atomically thin form (monolayer) compared to its bulk form. In that sense it is similar to graphene and transition metal dichalcogenides(TMDC) which have recently attracted great attention since it became possible to make atomically flat 2D materials of them via exfoliation. Exfoliation of V$_2$O$_5$ has not yet been successful to monolayer thicknesses, but efforts to do so are currently on-going and the goal of our work is to predict and explore if it would have interesting properties in monolayer form. However, V$_2$O$_5$ is very different from graphene and TMDC because it has a different crystal structure (orthorhombic instead of hexagonal) and is an oxide with transition metal atoms with $d$-like conduction bands in which strongly correlated effects could occur. An additional interest stems from the fact that its crystal structure contains 1D chains in the layers, so it may exhibit also 1D physical aspects. Besides this motivation in terms of 2D physics, V$_2$O$_5$ has numerous potential applications in catalysis, Li-ion batteries, electrochromic behavior, electro mechanical phenomena etc. and can exhibit various nanoforms. In this dissertation we first focus on the phonons or vibrational modes. Important changes in the vibrational modes were known to occur in TMDCs in monolayer form and our goal was to see if this is also true in V$_2$O$_5$. We first reproduced the phonon spectra (Raman and Infrared) in bulk V$_2$O$_5$ and reanalyzed the existing experimental literature to demonstrate the accuracy of our computational approach. We then focused on the changes induced between bulk and monolayer V$_2$O$_5$ and explained them in terms of a detailed analysis of the force constants. An important conclusion is that the difference in screening in 2D from 3D materials leads to changes in the long-range dipolar type forces which affect the phonon frequencies. Next, we focused on the electronic energy band structure. The unique and already known feature of the V$_2$O$_5$ band structure is that its lowest conduction band is a separate narrow $d$-band. We further analyzed this and then explored how the recently developed QS$GW$ method affects the band structure. To our surprise the band gap in QS$GW$ is strongly overestimated compared to experiment. This is unusual and required us to delve into the origins of this discrepancy. We explored in particular the effect of the lattice polarization on the screening of the Coulomb interaction $W$ in the $GW$ theory. In a first step we estimated this as a simple correction factor for the change in self-energy. We then applied the same scheme to the monolayer and also to doped V$_2$O$_5$. This correction factor comes out approximately 38 \% for bulk and 50 \% for monolayer respectively. Applying this simple correction factor to the self-energy, surprisingly it gives the $GW$ band gap 2.3 eV very close to the experimental value. Similar correction factor is also applied to doped V$_2$O$_5$. Doping of V$_2$O$_5$ as occurs in NaV$_2$O$_5$ is of great interest because then the lowest narrow conduction band becomes partially filled and can exhibit interesting transport as well as magnetic and new optical effects. NaV$_2$O$_5$ is known to exist in a ferromagnetic phase at room temperature(above 34 K). However, there are still ambiguities in the literature between theory and experiments about the origin and properties of the spin-gapped phase at low temperature, i.e., below 34 K. We first revisit the usual LSDA and LSDA+$U$ calculations and also use QS$GW$ with similar correction factor as in pure V$_2$O$_5$ to address the band structure, optical properties and antiferromagnetism of NaV$_2$O$_5$. First, we find indeed that half-filling of the band leads to a splitting of up and down spins in the split-off band and hence the formation of magnetic moments (if Hubbard $U'$s are included or the electron-electron interaction is described at the $GW$ level). Second we find that these moments prefer to couple antiferromagnetically along the chain and then lead to a much reduced dispersion of the split-off bands along the chain direction. Other splittings in the low conduction bands occur and lead to new optical transitions compared to pure V$_2$O$_5$, which we compared favorably to experiments. We find that the first peak in the optical conductivity data for $E\parallel a$ is very strong and corresponds to a transition from the bonding to the antibonding states with the same spin in a single rung. For $E\parallel b$ the transition is weaker and corresponds to the transition between bonding to antibonding with the same spin but in different rungs. Secondly, we determined the exchange interactions between V atoms by mapping the total energy differences of various magnetic configurations to a Heisenberg like model. We find that both the interaction between V in the same chain and between V in adjacent chains are antiferromagnetic and contribute both to the net antiferromagnetic coupling between rungs. Finally, we studied how the properties of doped V$_2$O$_5$ would change with continuously tuned electron doping, away from exactly half-filling of the split-off band. We did this in several different ways: either by adding a homogeneous background charge density or by changing the atomic number of the V atoms or the atomic number of the Na in the case of NaV$_2$O$_5$. These last two approaches constitute a virtual crystal approximation. We found that these different approaches affect the band structure differently because of the changes in electrostatic effects of the compensating charge. The model with VCA for Na is deemed to represent doping by gating the most accurately because the positive charges compensating the inserted electrons are then most separated from the V$_2$O$_5$ layer. We find that at Z$_{Na}$=10.88, which simulates a reduced concentration of Na or only 88 \% of the half-filling electron concentration the coupling among nearest neighbor V along the chains switches from antiferromagnetic to ferromagnetic coupling. This is explained in terms of the Anderson-Hasegawa model as a switch from AFM superexchange to FM double exchange via the intervening oxygen. Finally we returned to the question of lattice polarization in $GW$ and studied its impact in a more accurate implementation of the effect. We implemented the lattice polarisation effect with proper treatment of the anisotropy and wave vector dependence in the $GW$. In particular, we now take into account that this effect only exists in the long-wavelength limit ${\bf q}\rightarrow 0$ and in the static limit $\omega\rightarrow0$. We tested the approach for MgO, NaCl and SrTiO$_3$ before applying it to V$_2$O$_5$. We find that the correction is now much smaller than what we had expected in our first observation only 0.2 eV. We therefore conclude that other effects such as: electron-hole interaction, electron phonon coupling and other higher order diagrams in the expansion of the screened Coulomb interaction need to be considered.
Walter Lambrecht, Prof. (Advisor)
193 p.
Physics
Two dimensional; bulk and monolayer; phonons; red and blue shift; Born-effective charge; QSGW band gap; lattice polarisation effect; Lyddane-Sachs-Teller; half-filled one dimensional Hubbard chain; spin-Pierels transition; strongly correlated system; AFM

Recommended Citations

Citations

  • BHANDARI, C. B. (2016). FIRST-PRINCIPLES STUDY OF ELECTRONIC AND VIBRATIONAL PROPERTIES OF BULK AND MONOLAYER V2O5 [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1459296089

    APA Style (7th edition)

  • BHANDARI, CHURNA. FIRST-PRINCIPLES STUDY OF ELECTRONIC AND VIBRATIONAL PROPERTIES OF BULK AND MONOLAYER V2O5. 2016. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1459296089.

    MLA Style (8th edition)

  • BHANDARI, CHURNA. "FIRST-PRINCIPLES STUDY OF ELECTRONIC AND VIBRATIONAL PROPERTIES OF BULK AND MONOLAYER V2O5." Doctoral dissertation, Case Western Reserve University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=case1459296089

    Chicago Manual of Style (17th edition)

case1459296089
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This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.